<h2>题目编号 : 86</h2>
<div style="color:#666;font-size:80%;">07 January 2005</div><br />
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<p>A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner. By travelling on the surfaces of the room the shortest &quot;straight line&quot; distance from S to F is 10 and the path is shown on the diagram.</p>
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<img src="project/images/p_086.gif" alt="" /><br />
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<p>However, there are up to three &quot;shortest&quot; path candidates for any given cuboid and the shortest route is not always integer.</p>
<p>By considering all cuboid rooms with integer dimensions, up to a maximum size of M by M by M, there are exactly 2060 cuboids for which the shortest distance is integer when M=100, and this is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions is 1975 when M=99.</p>
<p>Find the least value of M such that the number of solutions first exceeds one million.</p>

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